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REAL FUNCTION PCQRT14( TRANS, M, N, NRHS, A, IA, JA,
$ DESCA, X, IX, JX, DESCX, WORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER IA, IX, JA, JX, M, N, NRHS
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCX( * )
COMPLEX A( * ), WORK( * ), X( * )
* ..
*
* Purpose
* =======
*
* PCQRT14 checks whether sub( X ) is in the row space of sub( A ) or
* sub( A )', where sub( A ) denotes A( IA:IA+M-1, JA:JA+N-1 ) and
* sub( X ) denotes X( IX:IX+N-1, JX:JX+NRHS-1 ) if TRANS = 'N', and
* X( IX:IX+N-1, JX:JX+NRHS-1 ) otherwise. It does so by scaling both
* sub( X ) and sub( A ) such that their norms are in the range
* [sqrt(eps), 1/sqrt(eps)], then computing an LQ factorization of
* [sub( A )',sub( X )]' (if TRANS = 'N') or a QR factorization of
* [sub( A ),sub( X )] otherwise, and returning the norm of the trailing
* triangle, scaled by MAX(M,N,NRHS)*eps.
*
* Notes
* =====
*
* Each global data object is described by an associated description
* vector. This vector stores the information required to establish
* the mapping between an object element and its corresponding process
* and memory location.
*
* Let A be a generic term for any 2D block cyclicly distributed array.
* Such a global array has an associated description vector DESCA.
* In the following comments, the character _ should be read as
* "of the global array".
*
* NOTATION STORED IN EXPLANATION
* --------------- -------------- --------------------------------------
* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
* DTYPE_A = 1.
* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
* the BLACS process grid A is distribu-
* ted over. The context itself is glo-
* bal, but the handle (the integer
* value) may vary.
* M_A (global) DESCA( M_ ) The number of rows in the global
* array A.
* N_A (global) DESCA( N_ ) The number of columns in the global
* array A.
* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
* the rows of the array.
* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
* the columns of the array.
* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
* row of the array A is distributed.
* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
* first column of the array A is
* distributed.
* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
* array. LLD_A >= MAX(1,LOCr(M_A)).
*
* Let K be the number of rows or columns of a distributed matrix,
* and assume that its process grid has dimension p x q.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the p processes of its
* process column.
* Similarly, LOCc( K ) denotes the number of elements of K that a
* process would receive if K were distributed over the q processes of
* its process row.
* The values of LOCr() and LOCc() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
* An upper bound for these quantities may be computed by:
* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
* Arguments
* =========
*
* TRANS (global input) CHARACTER*1
* = 'N': No transpose, check for sub( X ) in the row space of
* sub( A ),
* = 'C': Conjugate transpose, check for sub( X ) in row space
* of sub( A )'.
*
* M (global input) INTEGER
* The number of rows to be operated on, i.e. the number of rows
* of the distributed submatrix sub( A ). M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on, i.e. the number of
* columns of the distributed submatrix sub( A ). N >= 0.
*
* NRHS (global input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the distributed submatrix sub( X ). NRHS >= 0.
*
* A (local input) COMPLEX pointer into the local memory
* to an array of dimension (LLD_A, LOCc(JA+N-1)). This array
* contains the local pieces of the M-by-N distributed matrix
* sub( A ).
*
* IA (global input) INTEGER
* The row index in the global array A indicating the first
* row of sub( A ).
*
* JA (global input) INTEGER
* The column index in the global array A indicating the
* first column of sub( A ).
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* X (local input) COMPLEX pointer into the local
* memory to an array of dimension (LLD_X,LOCc(JX+NRHS-1)).
* On entry, this array contains the local pieces of the
* N-by-NRHS distributed submatrix sub( X ) if TRANS = 'N',
* and the M-by-NRHS distributed submatrix sub( X ) otherwise.
*
* IX (global input) INTEGER
* The row index in the global array X indicating the first
* row of sub( X ).
*
* JX (global input) INTEGER
* The column index in the global array X indicating the
* first column of sub( X ).
*
* DESCX (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix X.
*
* WORK (local workspace) COMPLEX array dimension (LWORK)
* If TRANS='N', LWORK >= MNRHSP * NQ + LTAU + LWF and
* LWORK >= MP * NNRHSQ + LTAU + LWF otherwise, where
*
* IF TRANS='N', (LQ fact)
* MNRHSP = NUMROC( M+NRHS+IROFFA, MB_A, MYROW, IAROW,
* NPROW )
* LTAU = NUMROC( IA+MIN( M+NRHS, N )-1, MB_A, MYROW,
* RSRC_A, NPROW )
* LWF = MB_A * ( MB_A + MNRHSP + NQ0 )
* ELSE (QR fact)
* NNRHSQ = NUMROC( N+NRHS+ICOFFA, NB_A, MYCOL, IACOL,
* NPCOL )
* LTAU = NUMROC( JA+MIN( M, N+NRHS )-1, NB_A, MYCOL,
* CSRC_A, NPCOL )
* LWF = NB_A * ( NB_A + MP0 + NNRHSQ )
* END IF
*
* and,
*
* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* MP0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
* NQ0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ).
*
* INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL ONE, ZERO
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL TPSD
INTEGER IACOL, IAROW, ICOFFA, ICTXT, IDUM, IIA, INFO,
$ IPTAU, IPW, IPWA, IROFFA, IWA, IWX, J, JJA,
$ JWA, JWX, LDW, LWORK, MPWA, MPW, MQW, MYCOL,
$ MYROW, NPCOL, NPROW, NPW, NQWA, NQW
REAL ANRM, ERR, XNRM
COMPLEX AMAX
* ..
* .. Local Arrays ..
INTEGER DESCW( DLEN_ ), IDUM1( 1 ), IDUM2( 1 )
REAL RWORK( 1 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER NUMROC
REAL PCLANGE, PSLAMCH
EXTERNAL LSAME, NUMROC, PCLANGE, PSLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCMAX1,
$ PCCOPY, PCGELQF, PCGEQRF, PCLACGV,
$ PCLACPY, PCLASCL, PXERBLA, SGAMX2D
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD, REAL
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
PCQRT14 = ZERO
*
IPWA = 1
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
IWA = IROFFA + 1
JWA = ICOFFA + 1
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA,
$ JJA, IAROW, IACOL )
MPWA = NUMROC( M+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQWA = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
*
INFO = 0
IF( LSAME( TRANS, 'N' ) ) THEN
IF( N.LE.0 .OR. NRHS.LE.0 )
$ RETURN
TPSD = .FALSE.
MPW = NUMROC( M+NRHS+IROFFA, DESCA( MB_ ), MYROW, IAROW,
$ NPROW )
NQW = NQWA
*
* Assign descriptor DESCW for workspace WORK and pointers to
* matrices sub( A ) and sub( X ) in workspace
*
IWX = IWA + M
JWX = JWA
LDW = MAX( 1, MPW )
CALL DESCSET( DESCW, M+NRHS+IROFFA, N+ICOFFA, DESCA( MB_ ),
$ DESCA( NB_ ), IAROW, IACOL, ICTXT, LDW )
*
ELSE IF( LSAME( TRANS, 'C' ) ) THEN
IF( M.LE.0 .OR. NRHS.LE.0 )
$ RETURN
TPSD = .TRUE.
MPW = MPWA
NQW = NUMROC( N+NRHS+ICOFFA, DESCA( NB_ ), MYCOL, IACOL,
$ NPCOL )
*
* Assign descriptor DESCW for workspace WORK and pointers to
* matrices sub( A ) and sub( X ) in workspace
*
IWX = IWA
JWX = JWA + N
LDW = MAX( 1, MPW )
CALL DESCSET( DESCW, M+IROFFA, N+NRHS+ICOFFA, DESCA( MB_ ),
$ DESCA( NB_ ), IAROW, IACOL, ICTXT, LDW )
ELSE
CALL PXERBLA( ICTXT, 'PCQRT14', -1 )
RETURN
END IF
*
* Copy and scale sub( A )
*
IPTAU = IPWA + MPW*NQW
CALL PCLACPY( 'All', M, N, A, IA, JA, DESCA, WORK( IPWA ), IWA,
$ JWA, DESCW )
RWORK( 1 ) = ZERO
ANRM = PCLANGE( 'M', M, N, WORK( IPWA ), IWA, JWA, DESCW, RWORK )
IF( ANRM.NE.ZERO )
$ CALL PCLASCL( 'G', ANRM, ONE, M, N, WORK( IPWA ), IWA,
$ JWA, DESCW, INFO )
*
* Copy sub( X ) or sub( X )' into the right place and scale it
*
IF( TPSD ) THEN
*
* Copy sub( X ) into columns jwa+n:jwa+n+nrhs-1 of work
*
DO 10 J = 1, NRHS
CALL PCCOPY( M, X, IX, JX+J-1, DESCX, 1, WORK( IPWA ), IWX,
$ JWX+J-1, DESCW, 1 )
10 CONTINUE
XNRM = PCLANGE( 'M', M, NRHS, WORK( IPWA ), IWX, JWX, DESCW,
$ RWORK )
IF( XNRM.NE.ZERO )
$ CALL PCLASCL( 'G', XNRM, ONE, M, NRHS, WORK( IPWA ), IWX,
$ JWX, DESCW, INFO )
*
* Compute QR factorization of work(iwa:iwa+m-1,jwa:jwa+n+nrhs-1)
*
MQW = NUMROC( M+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IPW = IPTAU + MIN( MQW, NQW )
LWORK = DESCW( NB_ ) * ( MPW + NQW + DESCW( NB_ ) )
CALL PCGEQRF( M, N+NRHS, WORK( IPWA ), IWA, JWA, DESCW,
$ WORK( IPTAU ), WORK( IPW ), LWORK, INFO )
*
* Compute largest entry in upper triangle of
* work(iwa+n:iwa+m-1,jwa+n:jwa+n+nrhs-1)
*
ERR = ZERO
IF( N.LT.M ) THEN
DO 20 J = JWX, JWA+N+NRHS-1
CALL PCMAX1( MIN(M-N,J-JWX+1), AMAX, IDUM, WORK( IPWA ),
$ IWA+N, J, DESCW, 1 )
ERR = MAX( ERR, ABS( AMAX ) )
20 CONTINUE
END IF
CALL SGAMX2D( ICTXT, 'All', ' ', 1, 1, ERR, 1, IDUM1, IDUM2,
$ -1, -1, 0 )
*
ELSE
*
* Copy sub( X )' into rows iwa+m:iwa+m+nrhs-1 of work
*
DO 30 J = 1, NRHS
CALL PCCOPY( N, X, IX, JX+J-1, DESCX, 1, WORK( IPWA ),
$ IWX+J-1, JWX, DESCW, DESCW( M_ ) )
CALL PCLACGV( N, WORK( IPWA ), IWX+J-1, JWX, DESCW,
$ DESCW( M_ ) )
30 CONTINUE
*
XNRM = PCLANGE( 'M', NRHS, N, WORK( IPWA ), IWX, JWX, DESCW,
$ RWORK )
IF( XNRM.NE.ZERO )
$ CALL PCLASCL( 'G', XNRM, ONE, NRHS, N, WORK( IPWA ), IWX,
$ JWX, DESCW, INFO )
*
* Compute LQ factorization of work(iwa:iwa+m+nrhs-1,jwa:jwa+n-1)
*
NPW = NUMROC( N+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
IPW = IPTAU + MIN( MPW, NPW )
LWORK = DESCW( MB_ ) * ( MPW + NQW + DESCW( MB_ ) )
CALL PCGELQF( M+NRHS, N, WORK( IPWA ), IWA, JWA, DESCW,
$ WORK( IPTAU ), WORK( IPW ), LWORK, INFO )
*
* Compute largest entry in lower triangle in
* work(iwa+m:iwa+m+nrhs-1,jwa+m:jwa+n-1)
*
ERR = ZERO
DO 40 J = JWA+M, MIN( JWA+N-1, JWA+M+NRHS-1 )
CALL PCMAX1( JWA+M+NRHS-J, AMAX, IDUM, WORK( IPWA ),
$ IWX+J-JWA-M, J, DESCW, 1 )
ERR = MAX( ERR, ABS( AMAX ) )
40 CONTINUE
CALL SGAMX2D( ICTXT, 'All', ' ', 1, 1, ERR, 1, IDUM1, IDUM2,
$ -1, -1, 0 )
*
END IF
*
PCQRT14 = ERR / ( REAL( MAX( M, N, NRHS ) ) *
$ PSLAMCH( ICTXT, 'Epsilon' ) )
*
RETURN
*
* End of PCQRT14
*
END
|
